It is worthwhile to mention that the optical theorem imposes a severe condition to achieve ZFS. This theorem of optics relates the extinction cross section \(\sigma ^{ext}\)  to the forward scattering amplitude \(s_\theta (0,0)\)  and can be expressed as \(\sigma ^{ext}= \frac{\lambda ^2_0}{\pi } {\rm Im}[s_\theta (0,0)] \)  [1]}, [2]}. In practice, \(Q_f=0\)  (at 2nd Kerker's condition) appears by achieving \(a_1=-b_1\)  without necessarily making both of them zero [3]}, which not only vanishes the forward scattering but also nullify the total extinction cross section (one may refer to Eq. (REF ) in quasi-static approximation). Subsequently, the non zero \(a_1\)  and \(b_1\)  are implying that the overall scattering in all
other directions may still be significantly different from zero, which seems to be a contradiction to the fact that extinction cross section vanishes.
However, the usual approximation for the dipole coefficients fail to satisfy energy conservation requirements [1]}. A more accurate approximation for those coefficients, taking into account radiative corrections, shows that the forward scattering is not exactly zero, relaxing the contradiction.
Therefore, one cannot completely suppress the forward scattering, it may be possible to achieve near zero forward scattering (NZFS) at second Kerker's condition.
In order to demonstrate these conditions, we use the effective medium theory that will provide an environment to satisfy the Kerker's conditions.
